THE MEAN-MEDIAN-MODE INEQUALITY: COUNTEREXAMPLES

Karim M. Abadir

Econometric Theory, 2005, vol. 21, issue 2, 477-482

Abstract: Let x be a random variable whose first three moments exist. If the density of x is unimodal and positively skewed, then counterexamples are provided which show that the inequality mode ≤ median ≤ mean does not necessarily hold.I thank Andrey Vasnev for help with the graphs and Jan Magnus for various helpful discussions. I also thank Martin Bland, Paolo Paruolo, Peter Phillips, Michael Rockinger, and a referee for their comments. ESRC grant R000239538 is gratefully acknowledged.

Date: 2005
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